K12n47
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^5-4 q^4+6 q^3-8 q^2+9 q-9+8 q^{-1} -6 q^{-2} +4 q^{-3} -2 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-9 t^2+13 t-11+13 t^{-1} -9 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+3 z^4-5 z^2+1 }[/math] |
| Determinant | 59 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-2 a^2 z^4+3 z^4 a^{-2} -z^4 a^{-4} +3 z^4+a^4 z^2-6 a^2 z^2+z^2 a^{-2} -3 z^2 a^{-4} +2 z^2+2 a^4-3 a^2- a^{-4} + a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+2 a^3 z^9+5 a z^9+3 z^9 a^{-1} +a^4 z^8-a^2 z^8+4 z^8 a^{-2} +2 z^8-11 a^3 z^7-22 a z^7-7 z^7 a^{-1} +4 z^7 a^{-3} -6 a^4 z^6-13 a^2 z^6-8 z^6 a^{-2} +3 z^6 a^{-4} -18 z^6+19 a^3 z^5+28 a z^5+2 z^5 a^{-1} -6 z^5 a^{-3} +z^5 a^{-5} +12 a^4 z^4+29 a^2 z^4+z^4 a^{-2} -3 z^4 a^{-4} +21 z^4-11 a^3 z^3-12 a z^3-4 z^3 a^{-1} +3 z^3 a^{-5} -9 a^4 z^2-17 a^2 z^2-z^2 a^{-2} +3 z^2 a^{-4} +3 z^2 a^{-6} -9 z^2+2 a^3 z+2 a z+2 z a^{-1} +z a^{-3} -z a^{-5} +2 a^4+3 a^2- a^{-4} - a^{-6} +2 }[/math] |
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